by
Hall, Prentice

Answer

7 singing acts
5 comedy acts

Work Step by Step

Let s be the number of singing acts, and let c be the number of comedy acts.
The show has 12 acts, so:
$s+c=12$
The show lasts 50 minutes. Using the lengths given for each show:
$5s+3c=50$
Step 1: Solve for s in the first equation.
$s+c=12$
$s+c-c=12-c$
$s=12-c$
Step 2: Substitute "$12-c$" for s in the second equation and solve for c.
$5s+3c=50$
$5(12-c)+3c=50$
$60-5c+3c=50$
$60-2c-60=50-60$
$-2c=-10$
$-2c\div-2=-10\div-2$
$c=5$
Step 3: Substitute 5 for c in the first equation and solve for s.
$s+c=12$
$s+5=12$
$s+5-5=12-5$
$s=7$
Substitute the values into each equation to check the answer.
$s+c=12$
$7+5=12\checkmark$
$5s+3c=50$
$5(7)+3(5)=50$
$35+15=50$
$50=50\checkmark$